We outline the rationale and preliminary results of using the State Context Property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used, and combined to generate meaning. The quantum formalism was developed to cope with problems arising in the description of (1) the measurement process, and (2) the generation of new states with new properties when particles become entangled. Similar problems arising with concepts motivated the formal treatment introduced (...) here. Concepts are viewed not as fixed representations, but entities existing in states of potentiality that require interaction with a context---a stimulus or another concept---to `collapse' to observable form as an exemplar, prototype, or other (possibly imaginary) instance. The stimulus situation plays the role of the measurement in physics, acting as context that induces a change of the cognitive state from superposition state to collapsed state. The collapsed state is more likely to consist of a conjunction of concepts for associative than analytic thought because more stimulus or concept properties take part in the collapse. We provide two contextual measures of conceptual distance---one using collapse probabilities and the other weighted properties---and show how they can be applied to conjunctions using the pet fish problem. (shrink)

The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the cognitive sphere (Aerts, Broekaert, & Smets, [Foundations of Science 1999, 4, 115–132; International Journal of Theoretical Physics, 2000, 38, 3231–3239]; Aerts and colleagues[Dialogue in Psychology, 1999, 10; Proceedings of Fundamental Approachs to Consciousness, Tokyo ’99; Mind in Interaction]. Basically, the intrinsic contextuality of the truth-value (...) of the Liar Paradox is appropriately covered by the abstracted quantum mechanical approach. The formal details of the model are explicited here for the generalized case. We prove the possibility of constructing a quantum model of the m-sentence generalizations of the Liar Paradox. This includes (i) the truth–falsehood state of the m-Liar Paradox can be represented by an embedded 2m-dimensional quantum vector in a (2m) m -dimensional complex Hilbert space, with cognitive interactions corresponding to projections, (ii) the construction of a continuous ‘time’ dynamics is possible: typical truth and falsehood value oscillations are described by Schrödinger evolution, (iii) Kirchoff and von Neumann axioms are satisfied by introduction of ‘truth-value by inference’ projectors, (iv) time invariance of unmeasured state. (shrink)

We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show (...) that the structure of the set of contexts and of the set of properties of a concept is a complete orthocomplemented lattice. The structural study in this article is a preparation for a numerical mathematical theory of concepts in the Hilbert space of quantum mechanics that allows the description of the combination of concepts. (shrink)

from non-conscious components by positing that consciousness is a universal primitive. For example, the double aspect theory of information holds that infor- mation has a phenomenal aspect. How then do you get from phenomenal infor- mation to human consciousness? This paper proposes that an entity is conscious to the extent it amplifies information, first by trapping and integrating it through closure, and second by maintaining dynamics at the edge of chaos through simul- taneous processes of divergence and convergence. The origin (...) of life through autocatalytic closure, and the origin of an interconnected worldview through conceptual closure, induced phase transitions in the degree to which informa- tion, and thus consciousness, is locally amplified. Divergence and convergence of cognitive information may involve phenomena observed in light e.g. focusing, interference, and resonance. By making information flow inward- biased, clo- sure shields us from external consciousness; thus the paucity of consciousness may be an illusion. (shrink)

We have recently theorized that consciousness is intrinsically connected to quantum mechanical spin since said spin is embedded in the microscopic structure of spacetime and is more fundamental than spacetime itself, that is, spin is the “mind-pixel.” Applying these ideas to the particular structures and dynamics of the brain, we have developed a qualitative model of quantum consciousness. In this paper, we express our fundamental view that spin is a primordial self-referential process driving quantum mechanics, spacetime dynamics and consciousness. To (...) justify such a view, we will draw support from existing literatures, discuss from a reductionist perspective the essential properties said spin should possess as mind-pixel and explore further the nature of spin to see whether said properties are present. Our conclusion is that these properties are indeed endowed to spin by Nature. One of the implications from our fundamental view is that the probabilistic structure of quantum mechanics is due to the self-referential collapse of spin state that is contextual, non-local, non-computable and irreversible. Therefore, a complete theory of the self-referential spin process is necessarily semantic, that is, it should be based on internally meaningful information. (shrink)

The paper describes an algorithm for semantic representation of behavioral contexts relative to a dichotomic decision alternative. The contexts are represented as quantum qubit states in two-dimensional Hilbert space visualized as points on the Bloch sphere. The azimuthal coordinate of this sphere functions as a one-dimensional semantic space in which the contexts are accommodated according to their subjective relevance to the considered uncertainty. The contexts are processed in triples defined by knowledge of a subject about a binary situational factor. The (...) obtained triads of context representations function as stable cognitive structure at the same time allowing a subject to model probabilistically-variative behavior. The developed algorithm illustrates an approach for quantitative subjectively-semantic modeling of behavior based on conceptual and mathematical apparatus of quantum theory. (shrink)